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Find the greatest common factor of 42,28 , and 70 .

Find the greatest common factor of $42$ , $28$ , and $70$ .

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Greatest common factor of three or four numbers

Full solution

Q. Find the greatest common factor of

42

,

28

, and

70

.

Factors of $42$ : List the factors of $42$ . $\newline$ To find the factors of $42$ , we look for pairs of numbers that multiply to give $42$ . $\newline$ $1 \times 42 = 42$ $\newline$ $2 \times 21 = 42$ $\newline$ $3 \times 14 = 42$ $\newline$ $6 \times 7 = 42$ $\newline$ Factors of $42$ : $1, 2, 3, 6, 7, 14, 21, 42$
Factors of $28$ : List the factors of $28$ . $\newline$ To find the factors of $28$ , we look for pairs of numbers that multiply to give $28$ . $\newline$ $1 \times 28 = 28$ $\newline$ $2 \times 14 = 28$ $\newline$ $4 \times 7 = 28$ $\newline$ Factors of $28$ : $1, 2, 4, 7, 14, 28$
Factors of $70$ : List the factors of $70$ . $\newline$ To find the factors of $70$ , we look for pairs of numbers that multiply to give $70$ . $\newline$ $1 \times 70 = 70$ $\newline$ $2 \times 35 = 70$ $\newline$ $5 \times 14 = 70$ $\newline$ $7 \times 10 = 70$ $\newline$ Factors of $70$ : $1, 2, 5, 7, 10, 14, 35, 70$
Common Factors of $42$ , $28$ , and $70$ : Identify the common factors of $42$ , $28$ , and $70$ . $\newline$ We look for factors that are present in all three lists. $\newline$ Factors of $42$ : $1$ , $2$ , $3$ , $6$ , $7$ , $14$ , $28$ $0$ , $42$ $\newline$ Factors of $28$ : $1$ , $2$ , $28$ $5$ , $7$ , $14$ , $28$ $\newline$ Factors of $70$ : $1$ , $2$ , $70$ $2$ , $7$ , $70$ $4$ , $14$ , $70$ $6$ , $70$ $\newline$ The common factors are: $1$ , $2$ , $7$ , $14$
Greatest Common Factor (GCF) of $42$ , $28$ , and $70$ : Find the greatest common factor (GCF) of $42$ , $28$ , and $70$ . $\newline$ The greatest number in the list of common factors is $14$ . $\newline$ GCF of $42$ , $28$ , and $70$ : $14$

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